Scores so far (updated 5/12 2pm)
Course information
https://piazza.com/csus/spring2020/csc28
Topics: Discrete structure definition and IEEE floating point representation as an example (including range, precision, and error).
Quiz: Wednesday January 29, based on your understanding of the following work.
Resources
Floating-point representation
Slides
Floating point visualizer (external link)
Topics: Notations (including “set-builder”), basic operations, Venn diagrams, Cartesian products, power sets, cardinality, countability, common numerical sets.
Quiz: Friday February 7, based on your understanding of the following work.
Resources
Book of Proof textbook
My notes
Topics: Propositional logic, logical connectives, truth tables, valid arguments (including modus ponens and modus tollens), logical equivalence, universal and existential quantification.
Quiz: Friday February 21, based on your understanding of the following work.
Resources
Book of Proof textbook
Logical equivalents
Logical inferences
My notes (logic)
My notes (quantifiers)
Topics: Boolean algebra, logic gates and combinational circuits, circuit design methodology, normal forms, reduction to nor/nand gates, circuit minimization, Karnaugh maps (including don’t care).
Quiz: Wednesday March 4, based on your understanding of the following work.
Resources
Topics: Implication (including converse, inverse, contrapositive), structure of formal proofs, direct proof, proof by contradiction, proof by induction, counterexamples.
Quiz: Friday March 20, based on your understanding of the following work.
Resources
Book of Proof textbook
My notes
Topics: Reflexivity, symmetry, transitivity, equivalence relations.
Quiz: Monday April 6, based on your understanding of the following work.
Activities
Read Chapter 11 of Book of Proof (22 pages)
Review the resources listed below
Reread Section 11.1 and do Exercises 1, 3, 5, 7, 10. (extra examples)
Reread Section 11.2 and do Exercises 1, 3, 5, 9, 11, 13, 15. (extra examples)
Reread Section 11.3 and do Exercises 1, 3, 5, 7. (extra examples)
Resources
YouTube: Relations between two sets (6:39)
YouTube: Relations and their Inverses (2:48)
YouTube: Reflexive, Symmetric, and Transitive Relations on a Set (6:53)
YouTube: You need to check EVERY spot for reflexivity, symmetry, and transitivity (3:39)
YouTube: Equivalence Relations (4:35)
YouTube: How to Prove a Relation is an Equivalence Relation (8:17)
Quiz Guide (solutions pdf, video)
Topics: Surjections, injections, inverses, composition, important functions in computer science (including modular reduction, “division algorithm”, floor, ceiling).
Quiz: Monday April 13, based on your understanding of the following work.
Activities
Read Chapter 12 of Book of Proof (20 pages)
Review the resources listed below
Reread Section 12.1 and do the odd Exercises (even solutions, video)
Reread Section 12.2 and do the Exercises 1, 3, 5, 7, 11 (even solutions, video)
Reread Section 12.4 and do the Exercises 1, 3, 5, 7 (even solutions, video)
Reread Section 12.5 and do the Exercises 1, 3, 5 (even solutions, video)
Reread Section 12.6 and do the Exercise 1
Do the problems on the worksheet: (worksheet, solutions)
Resources
Trefor Bazett Videos:
YouTube: The intuitive idea of a function (5:50)
YouTube: Formal Definition of a Function using the Cartesian Product (5:46)
YouTube: Is this relation a function? (5:08)
Khan Academy Videos:
YouTube: A more formal understanding of functions (16:01)
YouTube: Testing if a relationship is a function (2:22)
YouTube: Surjective (onto) and injective (one-to-one) functions (9:31)
YouTube: Relating invertibility to being onto and one-to-one (6:30)
YouTube: Creating new function from composition (2:56)
Quiz Guide (None this module – focus on Activities)
Topics: Sum and product rule, permutations, combinations, pigeonhole principle.
Quiz: Friday April 24, based on your understanding of the following work.
Activities
Read Chapter 3, Section 1–5 and 9 of Book of Proof (29 pages)
Review the resources listed below
Reread Sections 3.1 and 3.2 and do all odd Exercises (even solutions, video)
Reread Section 3.3 and do all odd Exercises (even solutions, video)
Reread Section 3.4 and do first five odd Exercises (even solutions, video)
Reread Section 3.5 and do first five odd Exercises (even solutions, video)
Reread Section 3.9 and do Exercises 1, 3 (3.9.2 solution)
Resources
Addition and multiplication rules introduction (pdf, video)
Quiz Guide (None this module – focus on Activities)
Topics: Languages and strings, deterministic finite automata, regular expressions.
Quiz: Monday May 4, based on your understanding of the following work.
Activities
Read Introduction 1 and Introduction 2
Review the resources listed below
Attempt these problems
After each problem, study its solution
Resources
Regular expression examples (slides, narration)
Finite automata examples (notes, Part I, Part II)
Online Tool
Quiz Guide
Topics: Problem solving with simple well-structured recursive functions, recursive mathematical functions, recursively defined sequences, using induction to prove recursive properties.
